Even though varieties of random walks have been proposed [1]} for single layer networks, only few exists for multiplex networks [2]} [3]}. We use three random walks procedures from the literature [2]}, [3]} defined for multiplex networks: Classical, Diffusive and Physical random walks. Furthermore, we add our multi-net random walk method to the existing multilayer random walk procedures and compare results in all experiments. Table REF  gives transition probabilities defined for each random walk methods. We define the following formula to sample the next neighbor either from the current layer or from another layer for the multi-net random walk in Equation  REF
\(\begin{aligned}P \big ( v_{n+1} = j_\beta \ | \ v_{n} = i_\alpha \big ) \ = \ \left\lbrace \begin{array}{ll}\frac{w_{ij}^{\gamma \gamma }}{c} \ if \ e_{i_\gamma ,j_\gamma } \in {E}_\gamma \ , \ i \ne j \\0 \ if \ i = j\end{array}\right.\end{aligned}\) 
